A: Good gravy, you've got one angry little critter!!
I am SO so sorry that you are so exhausted...I feel your pain through your writing. And it's no wonder - having two so close together - that is tough!
Well, he's definitely angry. And here's what I want you to do. Step back and really think about your interactions with him. I'm guessing they are 90% exasperated or angry...with reason. He acts like a toot, does NOT act lovable, so it's incredibly difficult to feel loving toward him, then he's dying for your attention... See a pattern here? On goes the cycle of doing whatever he can to get your attention - throwing, biting, etc. He's not even two, yet you've had a baby for nearly a year now - and babies demand our attention. That's just the way it is. And here he is, wondering how the heck he can get your love and attention away from the little one.
You are truly in a tough spot. Your baby needs you, but your big guy needs you as well. And the first thing he needs to feel secure is a strict schedule. And honey - you may as well forget restaurants and shopping unless you have a sitter - because that battle will be agonizing every time. Take a deep breath and roll with the fact that you are stuck without much of a life for a while. I promise it will get better - they get older and more independent, and one day you can actually go to the bathroom without wailing at the door. I swear, it happens!!
1. Get a routine. Strict schedule. Wake up, eat, play, eat, nap...same routine, same time, every day. Toddlers feel secure when they know what will come next and what to expect. Part of his problem may be the sleep issues - if you can get a routine down, sleeping should come easier. Toddlers that sleep well at night are set up to have better daytime behavior. So have a strict bedtime routine as well. Bath, two books ('two books' means two books!! - not three or four!), kiss, lights out. No deviations. He'll scream for water and heaven knows what else, but if you give in, you are training him that it works to scream. It has to stop. Do your best to make him feel loved and secure, but be firm with the bedtime routine.
2. You have GOT to find some consistent time to spend with him. Even thirty minutes a day. Color together, play with trucks, whatever. I know the baby will get sick, or not nap - things happen that muck up our day and your time with him will constantly be challenged, but make a serious effort. He is dying for your attention.
3. He CANNOT continue to get away with negative behavior. And here's where you are earning your medal in Mommy-ing. You have to have consistent, firm consequences that are the opposite of what he actually wants. You have to step back and figure out why he's throwing a fit, and give him the opposite. And girl, I know how hard this is when you've got a baby in tow - but until you can step back and be objective, your emotions will continue to monkey with effective discipline. If he (ie) throws his food, he must leave the table (and your attention) for a time out. And doing that darn time out dance with a baby in the wings will be a serious trick, but you've got to figure something out. He has to stay in time out - withOUT your attention - until he calms down. That means you have to make him stay put. Do what you must physically (pick him up, take him back to time out spot, or stand behind him to make him stay put, etc.,) but DO NOT look at him or talk - that is attention.
If you have any resources for help, use them. Having two that young is going to turn your hair gray, no matter how well behaved they are. Utilize help so that you can give them the individual attention that they need and keep some semblance of energy to keep up with the discipline.
My book would be a good resource for you (Toddler ABC Guide because it's a quick read), but finding the time to read it would be a bear. However, if you could, and you can change your thinking, utilize the strategies, and get yourself and the kids on a schedule, your life should be easier. It's just the mountain of getting there...and I get that.
In the meantime, 1) SCHEDULE, 2) time alone w/ him, 3) firm, consistent consequences (my book details this), and 4) keep your emotions in check. He cannot be reinforced for the negative behavior - and the more tired you are, the more likely you will give in. Just remember that giving in will make the future that much harder. You're not doing yourself any favors. And you certainly aren't doing him any favors, either. When he acts up, yet still gets what he wants, he is being trained that the behavior works. And 'getting what he wants' could mean you yelling or giving him any kind of attention at all. Remember, try to step back and be objective about the reason for the behavior.
Best of luck to you - you are in the middle of the marathon and just have to keep going. Wake up each day, do your best, and keep going. Crying is good sometimes - so is chocolate and hot tea. :) Talk with friends and remember to laugh. And don't worry about people looking at you. They aren't living your life and walking in your shoes, so they can just go fly a kite!